AxisAlgebra.mul_swap: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend as AxisAlgebra
Lines 209-213 of bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&start_line=209&end_line=213

import Base
import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as Nats

def mul_swap(+a: Nat, +b: Nat, +c: Nat) -> {Nat.mul(a, Nat.mul(b, c)) == Nat.mul(b, Nat.mul(a, c)) : Nat}:
  Equal.trans(Nat, Nat.mul(a, Nat.mul(b, c)), Nat.mul(Nat.mul(a, b), c), Nat.mul(b, Nat.mul(a, c)),
    Equal.sym(Nat, Nat.mul(Nat.mul(a, b), c), Nat.mul(a, Nat.mul(b, c)), Nats.mul_assoc(a, b, c)),
    Equal.trans(Nat, Nat.mul(Nat.mul(a, b), c), Nat.mul(Nat.mul(b, a), c), Nat.mul(b, Nat.mul(a, c)),
      Equal.cong(Nat, Nat, n => Nat.mul(n, c), Nat.mul(a, b), Nat.mul(b, a), Nats.mul_comm(a, b)), Nats.mul_assoc(b, a, c)))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend&name=mul_assoc
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend&name=mul_comm